PRP Records

Probable Primes Top 10000

(252402 PRPs in the top)


What is a PRP ?

A PRP is a probable prime number, a number that nobody knows how to prove or disprove its primality.
Here are some criterions that can be used to recognize these numbers :

- N does not have any prime factor up to 2^32.
- N cannot be trivially written into a product.
- Take 3 square-free consecutive bases such that (b1/N)=(b2/N)=(b3/N)= -1. N should be such that b1^((N-1)/2)=b2^((N-1)/2)=b3^((N-1)/2)= -1 (mod N).
- Take a prime base such that (b/N)= -1 and b<>b1<>b2<>b3. N should pass the strong test in base b.
- or more (if someone has got an idea) !!!


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1-250   251-500   501-750   751-1000   1001-1250   1251-1500   1501-1750   1751-2000   
2001-2250   2251-2500   2501-2750   2751-3000   3001-3250   3251-3500   3501-3750   3751-4000   
4001-4250   4251-4500   4501-4750   4751-5000   5001-5250   5251-5500   5501-5750   5751-6000   
6001-6250   6251-6500   6501-6750   6751-7000   7001-7250   7251-7500   7501-7750   7751-8000   
8001-8250   8251-8500   8501-8750   8751-9000   9001-9250   9251-9500   9501-9750   9751-10000   


Rank Probable prime Digits (> 50000) Who ? When ?
9001(10^56781-31)/356781Serge Batalov12/2014
90027*10^56779+356780Erik Branger11/2009
900312858^13817-13817^1285856777Norbert Schneider11/2018
900410^56765+25917956766Patrick De Geest09/2013
900510^56765-24949756765Patrick De Geest09/2013
9006t(188706)56764Robert Price04/2015
90072^188551-90432756760Paul Bourdelais11/2012
9008(64*10^56756+17)/956757Robert Price09/2015
9009131101#+14629156757Makoto Morimoto02/2016
90102^188539-11251956756Enzo Doria06/2014
90116^72927+10156749Lelio R Paula10/2012
901220^43617-160356748Enzo Doria03/2013
9013(3^118892-8)/9135892956718Lelio R Paula03/2012
901413339^13748-13748^1333956713Norbert Schneider09/2018
9015(509203*2^188338-1)/356701Lelio R Paula03/2015
901620^43567-562356682Enzo Doria03/2013
90172^188234-11318356665Enzo Doria07/2014
9018(139^26437+1)/14056653Richard Fischer03/2018
9019(7*2^188215-1)/149731512556651Lelio R Paula01/2014
9020(1017*2^188171-1)/3556647Lelio R Paula03/2015
9021(34*10^56647-7)/9/37/26356644Makoto Morimoto04/2016
9022(2^188176-1017)/45381454356638Lelio R Paula02/2012
902333*10^56634+756636Robert Price07/2016
9024(F(31)^9241-F(30)^9241)/F(29)56634Wayne Halsdorf08/2010
902514^49413+3356634Lelio R Paula02/2013
90263^118680+11056625Lelio R Paula10/2012
9027(13*10^56624+161)/356625Robert Price04/2017
9028(3^118676-2)/751665326356613Lelio R Paula03/2012
9029(13*2^188062+1)/1756613Lelio R Paula07/2012
90302^188056-131356611Yves Minet08/2012
903120^43510-558356608Enzo Doria03/2013
90322^188032+1228556604Lelio R Paula03/2011
9033(19*10^56597-43)/356598Robert Price10/2017
9034(265*10^56588+17)/356590Robert Price05/2016
90352^187959+577556582Lelio R Paula03/2011
9036(5*2^187959+1)/5356581Lelio R Paula07/2012
90373*10^56575-1356576Robert Price11/2017
9038(11*2^187889-1)/35156559Lelio R Paula01/2014
9039(100049^11311+1)/10005056553Faysal YAtim09/2007
9040(19*10^56544-1)/956545Serge Batalov03/2009
904120^43447-892356526Enzo Doria03/2013
904210423^14066-14066^1042356518Norbert Schneider11/2018
90432^187743-11217756517Enzo Doria06/2014
9044(F(5879)^47-F(5878)^47)/F(5877)56502Wayne Halsdorf08/2010
90455^80831-2256499Lelio R Paula10/2012
90465^80828-1316656497Enzo Doria02/2013
90477*2^187590-556472Lelio R Paula03/2014
90482^187555+7547356460Enzo Doria04/2016
90492^187541-28356456Yves Minet01/2012
9051(55*10^56453-1)/956454Serge Batalov03/2009
905012933^13730-13730^1293356454Norbert Schneider09/2018
90522^187506-145156445Yves Minet08/2012
9053189^24794-256443Lelio R Paula10/2017
905413600^13653-13653^1360056436Norbert Schneider08/2018
90556^72522+14356434Lelio R Paula10/2012
9056(15185*2^187452-1)/94956430Lelio R Paula03/2015
90572^187390+7956411Lelio R Paula03/2011
90582^187386+1290956409Lelio R Paula03/2011
90592^187382+61356408Jason Earls04/2008
9060(34*10^56392-7)/9/37/883/2388756384Makoto Morimoto04/2016
906120^43337-956383Lelio R Paula02/2013
9062(26*10^56371-173)/356372Robert Price10/2017
9063(F(1008)^269-F(1007)^269)/F(1006)56364Wayne Halsdorf08/2010
90652^187230+42756362Henri Lifchitz01/2005
906411^54121-948056362Enzo Doria02/2013
906610758^13979-13979^1075856360Norbert Schneider09/2018
906710635^13996-13996^1063556359Norbert Schneider09/2018
9068(21*2^187202-1)/4356354Lelio R Paula01/2014
90692^187173-9156345Lelio R Paula03/2011
9070(23*2^187174-1)/2071988356340Lelio R Paula01/2014
90712^187125-283356331Yves Minet09/2014
90729*7^66655-456331Lelio R Paula09/2014
907418^44874-9756330Lelio R Paula02/2013
907313304^13659-13659^1330456330Norbert Schneider08/2018
907560*79^29679+1956322Serge Batalov03/2016
90765^80571+5656317Lelio R Paula10/2012
90775^80551-2256303Lelio R Paula10/2012
9078(76*10^56281+41)/956282Robert Price10/2015
9079(88*10^56271-43)/956272Robert Price11/2015
9080(5*10^56256-119)/356257Robert Price04/2016
90811508^17691+17691^150856230Serge Batalov05/2014
90823^117844-5856226Lelio R Paula10/2012
9083(19*10^56224+737)/956225Robert Price10/2017
908495^28427+256221Lelio R Paula05/2013
90852^186713+7681756207Enzo Doria05/2016
908616534^2505+2505^1653456196Hans Havermann06/2016
908714428^7849+7849^1442856195Hans Havermann06/2016
90882*10^56194-5156195Robert Price11/2017
908914898^5909+5909^1489856189Hans Havermann06/2016
909018^44758+9556184Lelio R Paula02/2013
90917478^14503-14503^747856182Norbert Schneider11/2018
90922^186555-74156159Lelio R Paula05/2011
9093(4*10^56156+173)/356157Robert Price01/2017
9095(3^117708+7)/44789656156Lelio R Paula03/2012
909415711^3752+3752^1571156156Hans Havermann06/2016
9096(23*2^186549-1)/242902556152Lelio R Paula01/2014
9097387^21694+21694^38756138Norbert Schneider08/2014
90982^186422+1723956119Yves Minet01/2010
90992^186418+424242956118Jason Earls10/2008
9100136^26300+13556113Norbert Schneider04/2015
91015*2^186392+956111Lelio R Paula03/2014
910214345^8152+8152^1434556108Hans Havermann07/2016
9103(5*2^186351-1)/3956097Lelio R Paula01/2014
91042^186319-54123756088Paul Bourdelais11/2012
91052*10^56083-4356084Robert Price07/2017
9106(16*10^56082-61)/956083Serge Batalov05/2009
9107(14*10^56080-143)/356081Robert Price01/2017
9108(265*10^56076+17)/356078Robert Price05/2016
91097^66346-5056069Lelio R Paula10/2012
911020^43094-3356067Lelio R Paula02/2013
911120^43090-138356062Enzo Doria03/2013
91123^117482+266056054Lelio R Paula10/2012
9113(22699*2^186193+1)/11156052Lelio R Paula05/2014
9114(68*10^56042+13)/956043Ray Chandler09/2010
91153*6^71992+5^7199256022Mike Oakes03/2010
911613691^12352+12352^1369156020Hans Havermann07/2016
9117(2^186095+7)/7556019Lelio R Paula02/2012
9118247^23412+23412^24756018Norbert Schneider08/2014
91191839^17156+17156^183956008Serge Batalov05/2014
912013736^11949+11949^1373656007Hans Havermann04/2016
9121(5*2^186036-1)/1156003Lelio R Paula01/2014
9122(299*10^55998-17)/356000Robert Price01/2017
9123p(12103)#/2-12855994Robert Price05/2017
91242^186003-17433755993Gary Barnes09/2009
9125(2^186010+78557)/12355993Lelio R Paula05/2012
912620^43037-9355993Lelio R Paula02/2013
912716375^2626+2626^1637555991Hans Havermann03/2016
912811083^13842-13842^1108355987Norbert Schneider11/2018
912915631^3816+3816^1563155985Hans Havermann03/2016
913021^42335-255977Lelio R Paula08/2013
9131Phi(64736,139)55959Enzo Doria07/2012
913215215^4762+4762^1521555958Hans Havermann03/2016
913319317^788+788^1931755953Anatoly F. Selevich12/2006
913413582^13165+13165^1358255950Hans Havermann08/2016
9135(78557*2^185842+1)/18955947Lelio R Paula06/2014
913611867^13730-13730^1186755941Norbert Schneider09/2018
913715^47562-8655938Lelio R Paula02/2013
91384*10^55932+9155933Robert Price11/2017
91393^117222+455930Lelio R Paula03/2012
914024^40519-23^4051955925Robert Price07/2012
914113636^12623+12623^1363655924Hans Havermann07/2016
91422^185767-9955922Lelio R Paula03/2011
9143(19*2^185750-1)/1555917Lelio R Paula01/2014
914515^47542-5855914Lelio R Paula02/2013
914452211!4+255914Robert Price08/2017
914620^42973-558355910Enzo Doria03/2013
91474*10^55906+2155907Robert Price08/2016
91482^185713-11155906Lelio R Paula03/2011
914913^50174+8855891Lelio R Paula01/2013
915014569^6846+6846^1456955879Hans Havermann08/2016
9151Pell-LucasQ(145969)/255874Eric W. Weisstein08/2006
91523^117087-8055865Lelio R Paula10/2012
9153(7*10^55851-43)/955851Robert Price10/2014
91542^185519-16955847Lelio R Paula03/2011
91557^66074+1055840Lelio R Paula10/2012
9156(19*10^55833-49)/355834Robert Price02/2017
9157(2*10^55834-59)/355834Robert Price05/2017
91582^185463-423755830Yves Minet08/2018
915912^51732+555829Lelio R Paula01/2013
916011252^13779-13779^1125255822Norbert Schneider10/2018
91613*2^185429+755821Lelio R Paula03/2014
9162(60^31393+1)/6155820Paul Bourdelais08/2017
9163(9787*2^185420-1)/38155819Lelio R Paula04/2015
916414427^7396+7396^1442755819Hans Havermann08/2016
916510^55811+2155812Robert Price01/2011
916610^55811-7410355811Patrick De Geest12/2012
916711^53591-153055810Enzo Doria11/2012
9168(5^79841-5^39921+1)/1533415955800Lelio R Paula09/2017
91692^185355-214555798Lelio R Paula03/2011
917014531^6912+6912^1453155794Hans Havermann07/2016
91712^185327-161555789Lelio R Paula03/2011
91722^185280-1277955775Enzo Doria10/2012
917315504^3955+3955^1550455771Hans Havermann07/2016
9174(2*10^55762-59)/355762Robert Price05/2017
91755^79770-4455757Lelio R Paula10/2012
917618^44416-8555755Lelio R Paula02/2013
91772^185208-45999555754Enzo Doria06/2015
91782^185200+118555751Lelio R Paula03/2011
9179(536*10^55748-23)/955750Robert Price11/2017
91807^65964+6^(65964-1)55747Robert Price03/2016
91812^185151-23715755737Gary Barnes09/2009
9182110017^11055-10255734Enzo Doria07/2012
918314754^5987+5987^1475455729Hans Havermann07/2016
918412591^13592-13592^1259155729Norbert Schneider07/2018
918540090!3-955711Robert Price09/2014
91869*10^55707+8955708Robert Price11/2016
91872^185023-225755698Yves Minet06/2009
918818628^977+977^1862855696Anatoly F. Selevich01/2007
91892^185006-9355693Lelio R Paula03/2011
91902^185003-251555692Yves Minet07/2014
91912^184992-7855755689Jorge Menendez02/2018
91923*10^55679+3755680Robert Price10/2017
91936^71524-1955657Lelio R Paula10/2012
91942^184872-219555653Yves Minet08/2013
9195507^20572+20572^50755648Norbert Schneider06/2016
9196(86*10^55645-311)/955646Robert Price10/2017
9197134^26151-13355626Norbert Schneider03/2015
919815340^4221+4221^1534055614Hans Havermann07/2016
919927743!2+255612Robert Price01/2013
920020^42744+8155612Lelio R Paula02/2013
920114609^6406+6406^1460955611Hans Havermann07/2016
92022^184724-11288355608Enzo Doria06/2014
920313507^13074+13074^1350755601Hans Havermann07/2016
92042^184689+12955597Lelio R Paula03/2011
9205(9179*2^184672-1)/19355594Lelio R Paula03/2015
9206(22*10^55592-19)/355593Robert Price02/2017
9207Phi(59984,89)55582Enzo Doria05/2012
92088815^14088-14088^881555581Norbert Schneider11/2018
920911^53368+1655578Lelio R Paula01/2013
921020^42717-192355577Enzo Doria03/2013
9211117^26870+26870^11755573Serge Batalov05/2014
921212^51488+5555565Lelio R Paula01/2013
9213(44*10^55558-17)/955559Robert Price06/2015
9214(2*10^55559-23)/355559Robert Price09/2017
921510^55555+3285755556Patrick De Geest06/2010
921610^55555-13672155555Patrick De Geest06/2010
9217(11*2^184541-1)/35155551Lelio R Paula01/2014
921820^42696-204355549Enzo Doria03/2013
9219(35*10^55547-737)/955548Robert Price11/2017
9220(2*10^55544+1)/355544Serge Batalov06/2009
9221(-lucasV(1,2,369056)+2)/(3*89*109*457)55542Mike Oakes04/2017
92225003^15013-16055537Enzo Doria07/2012
922339^34896-255522Lelio R Paula08/2013
9224(6^71345-61)/555517Lelio R Paula05/2014
92252^184407-301955513Yves Minet10/2014
9226(43*10^55512-61)/955513Robert Price06/2015
922720^42667-84355512Enzo Doria03/2013
9228133^26134-13255505Norbert Schneider03/2015
9229(31*2^184378-1)/71155502Lelio R Paula01/2014
92309*7^65667-455497Lelio R Paula09/2014
92312^184342-17355493Lelio R Paula03/2011
923215^47182+9255491Lelio R Paula02/2013
92335^79378+655483Lelio R Paula10/2012
9234581^20068+20068^58155472Norbert Schneider06/2016
9235(2^184232+1)/25755457Donovan Johnson03/2005
923618^44177-141555455Enzo Doria03/2013
92372^184203-279786755451Enzo Doria04/2016
92382^184189+1755447Lelio R Paula03/2011
92392^184183+2612355445Yves Minet01/2010
9240Phi(77077,10)55441Ray Chandler05/2009
92412^184141-11325155432Enzo Doria07/2014
92422^184093-50461355418Gary Barnes09/2009
92436517^14528-14528^651755411Norbert Schneider12/2018
9244(lucasV(1,2,368167)+2)/(11*1103*1307*5647)55404Mike Oakes04/2017
92452^184044-11126955403Enzo Doria05/2014
924614051^8766+8766^1405155401Hans Havermann07/2016
924798^27819+27819^9855394Serge Batalov05/2014
9248(178*10^55390-7)/955392Robert Price08/2017
924958046^9+9^5804655390Andrey Kulsha02/2004
92507^65536+2*59232-255385Jiahao He07/2017


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: December, 17 2018 20:37 (Time in France)

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